Based on elementary linear algebra, we provide radically simplified proofs using quasiconformal changes of variables to obtain sharp constants and optimizers in cases of the Caffarelli-Kohn-Nirenberg inequality. Some of our results were obtained earlier by Lam and Lu.
All Science Journal Classification (ASJC) codes
- Caffarelli-Kohn-Nirenberg inequality
- Quasiconformal maps
- Sharp constants
- Weighted Sobolev inequality